Sofas are already known in the prior art comprising a headrest which is fitted such as to be able to pivot between two or more positions, in particular a lowered position and a raised position, in which it supports the head of the person seated on the sofa. It is also known to provide a system to control the displacement of the headrest between the two, raised and lowered positions, i.e. an electric system which controls the activation/deactivation of an electric motor which drives a mechanical system connected to the headrest. When the user wants to put the headrest into the position in which it supports his head, he commands the activation of the motor, in particular by means of control buttons, thus rotating the headrest until it reaches the required raised position. These sofas according to the prior art are quite complicated to use, and, in particular, each time the user sits down, he has to adjust the headrest to the appropriate position he wants, in particular by keeping a button pressed down, then, when he leaves the sofa, he has to lower the headrest to its lowered or rest position, in order to prevent the mechanical system connected to the headrest from being damaged by one impact or another, since when the headrest is in the raised position, the mechanical system is not protected as securely as when it is in the lowered position. In fact, in the lowered position, the mechanical system for displacement of the headrest does not appear on the exterior, and is therefore protected.